Final answer:
When a skater pulls their arms in and reduces their rotational inertia to half, their angular velocity doubles to conserve angular momentum.
Step-by-step explanation:
The question deals with the concept of conservation of angular momentum in physics. According to this principle, when a figure skater pulls their arms inward, they are reducing their rotational inertia. Since angular momentum is conserved (provided there is no net external torque acting on the system), a reduction in rotational inertia (I) results in an increase in angular velocity (ω).
If the skater's rotational inertia is reduced to half its original value, to conserve angular momentum (L = I*ω), the angular velocity must increase by a factor that compensates for the reduction in inertia. This means that the angular velocity would double, because (1/2)I * 2ω = I*ω, satisfying the conservation of angular momentum.